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Hi there,
I haven't fully read the article, but a quick comment would be that the
accuracy of frequency estimation of a single tone is not limited by the
uncertainty principle, human or machine alike. It is limited by Cramer-Rao
lower bound and I remember the mean square error of an optimal
frequency estimator is proportional to SNR/(time)^3, if the noise is
additive white Gaussian noise.
The uncertainty principle still governs the resolution of between time and
frequency **when multiple tones are present**. If two concurrent tones are
separated by delta_f, then it requires at least longer than 1/delta_f to
resolve the tones in the spectrum.
I'd be more interested to see if human pitch detection can violate the
Cramer-Rao bound.
Such is my two pennies,
Yi-Wen
On Saturday, February 16, 2013, Kevin Austin wrote:
> Comments?
>
>
> >> http://phys.org/news/2013-02-human-fourier-uncertainty-principle.html
> >>
> >>
> >> (Phys.org)=E2=80=94For the first time, physicists have found that huma=
ns can
> discriminate a sound's frequency (related to a note's pitch) and timing
> (whether a note comes before or after another note) more than 10 times
> better than the limit imposed by the Fourier uncertainty principle. Not
> surprisingly, some of the subjects with the best listening precision were
> musicians, but even non-musicians could exceed the uncertainty limit. The
> results rule out the majority of auditory processing brain algorithms tha=
t
> have been proposed, since only a few models can match this impressive hum=
an
> performance.
> >>
> >> Read more at:
> http://phys.org/news/2013-02-human-fourier-uncertainty-principle.html#jCp
>
>
> Thanks
>
> Kevin
--=20
Yi-Wen Liu =E5=8A=89=E5=A5=95=E6=B1=B6, Ph.D.
http://www.ee.nthu.edu.tw/ywliu/
"Silver and gold have I none; but such as I have give I thee."
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Hi there,=C2=A0<div><br></div><div>I haven&#39;t fully read the article, bu=
t a quick comment would be that the accuracy of=C2=A0frequency estimation o=
f a single tone is not limited by the uncertainty principle, human or machi=
ne alike. It is limited by Cramer-Rao lower bound and I remember the mean s=
quare error of an optimal frequency=C2=A0estimator=C2=A0is proportional to =
SNR/(time)^3, if the noise is additive white Gaussian noise.</div>
<div><br></div><div>The uncertainty principle still governs the resolution =
of between time and frequency **when multiple tones are present**. If two c=
oncurrent tones are separated by delta_f, then it requires at least longer =
than 1/delta_f to resolve the tones in the spectrum.=C2=A0</div>
<div><br></div><div>I&#39;d be more=C2=A0<span></span>interested to see if =
human pitch detection can violate the Cramer-Rao bound.</div><div><br></div=
><div>Such is my two pennies,</div><div><br></div><div>Yi-Wen</div><div><br=
>
On Saturday, February 16, 2013, Kevin Austin wrote:<br><blockquote class=
=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padd=
ing-left:1ex">Comments?<br>
<br>
<br>
&gt;&gt; <a href=3D"http://phys.org/news/2013-02-human-fourier-uncertainty-=
principle.html" target=3D"_blank">http://phys.org/news/2013-02-human-fourie=
r-uncertainty-principle.html</a><br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt; (Phys.org)=E2=80=94For the first time, physicists have found that =
humans can discriminate a sound&#39;s frequency (related to a note&#39;s pi=
tch) and timing (whether a note comes before or after another note) more th=
an 10 times better than the limit imposed by the Fourier uncertainty princi=
ple. Not surprisingly, some of the subjects with the best listening precisi=
on were musicians, but even non-musicians could exceed the uncertainty limi=
t. The results rule out the majority of auditory processing brain algorithm=
s that have been proposed, since only a few models can match this impressiv=
e human performance.<br>
&gt;&gt;<br>
&gt;&gt; Read more at: <a href=3D"http://phys.org/news/2013-02-human-fourie=
r-uncertainty-principle.html#jCp" target=3D"_blank">http://phys.org/news/20=
13-02-human-fourier-uncertainty-principle.html#jCp</a><br>
<br>
<br>
Thanks<br>
<br>
Kevin</blockquote></div><br><br>-- <br>Yi-Wen Liu =E5=8A=89=E5=A5=95=E6=B1=
=B6, Ph.D.<br><a href=3D"http://www.ee.nthu.edu.tw/ywliu/" target=3D"_blank=
">http://www.ee.nthu.edu.tw/ywliu/</a><br>&quot;Silver and gold have I none=
; but such as I have give I thee.&quot;<br>
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